1.

lim_(x to 2)((cos alpha)^(x) + (sin alpha)^(x)-1)/(x-2)=

Answer»

`(COS^(2) ALPHA) ln cos alpha + (SIN^(2) alpha)ln sin alpha`
1
`ln((cos alpha)(sin alpha))`
`ln((sin^(2) alpha) xx (cos^(2) alpha))`

SOLUTION :`lim_(x to 2)((cos alpha)^(x) + (sin alpha)^(x) - sin^(2) alpha - cos^(2) alpha)/(x-2)`
`lim_(x to 2) cos^(2) alpha ([cos^(x-2) alpha-1])/(x-2) + sin^(2)alpha ([sin^(x-2) alpha-1])/(x-2)`
`cos^(2) alpha.ln cos alpha + sin^(2) alpha ln sin alpha`


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